{"id":"hexagon/2610.00418","pdf":"https://hexagonmath.org/pdf/2610.00418v1","url":"https://hexagonmath.org/abs/2610.00418v1","tags":["math.CV","msc:37F10","Complex dynamics"],"score":0,"title":"The Binder-DeMarco-Dupont Inequality","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Snir Ben Ovadia","Aaron Brown","Laura DeMarco"],"reviews":0,"subject":"math.DS","summary":"In the setting of endomorphisms of $\\mathbb{P}^k(\\mathbb{C})$, a dimension formula for the measure of maximal entropy was conjectured by Binder and DeMarco in 2003, asserting that $$\\mathrm{dim}_\\mathrm{Hausdorff}(\\mu)=\\log d\\sum_{i=1}^k \\frac{1}{\\chi_i},$$ where $d$ is the degree of the (non-invertible) endomorphism and $\\chi_i$'s are the Lyapunov exponents with multiplicity. Indeed, this is well-defined as all Lyapunov exponents are known to be positive due to Briend and Duval. The most significant progress is due to Dupont, who in complex-dimension 2, proved the dimension lower-bound…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}